Cryptography Reference
In-Depth Information
Figure 10.13 - BER as a function of the signal to noise ratio
E
b
/N
0
of pragmatic turbo-
coded 16-QAM using a 16-state double-binary code. Transmission over a Gaussian
channel. Spectral eciency
η
=3
bit/s/Hz. Blocks of 15,000 information bits, 5,000
modulated symbols. MAP decoding algorithm. "systematic" scheme.
account the size of the blocks transmitted as well as the packet error rates (PER)
targeted. They are obtained from the value of the capacity of the channel, to
which we add a correcting term obtained with the help of the so-called "sphere
packing" bound, (see Section 3.3).
We observe that at high or average error rates, the convergence of the itera-
tive decoding process is favoured by a better protection of the systematic bits.
This result can be explained by the fact that, in the decoding process, each sys-
tematic data is used at the input of the two decoders. Consequently, an error on
a systematic bit at the output of the channel causes an error at the input of the
two elementary decoders, whereas erroneous redundancy only affects the input
of one of the two elementary decoders. Consequently, reinforcing the protection
of the systematic bits benefits the two elementary decoders simultaneously.
The higher the proportion of redundancy bits transmitted, that is to say,
thelowerthecodingrate,thegreaterthegapinperformancebetweenthetwo
